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Properties

Label 30899.f
Number of curves $3$
Conductor $30899$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 30899.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30899.f1 30899c3 \([0, 1, 1, -21967316, -39636368621]\) \(-52893159101157376/11\) \(-243807972419\) \([]\) \(748800\) \(2.4819\)  
30899.f2 30899c2 \([0, 1, 1, -29026, -3457281]\) \(-122023936/161051\) \(-3569592524186579\) \([]\) \(149760\) \(1.6771\)  
30899.f3 30899c1 \([0, 1, 1, -936, 25879]\) \(-4096/11\) \(-243807972419\) \([]\) \(29952\) \(0.87242\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30899.f have rank \(0\).

Complex multiplication

The elliptic curves in class 30899.f do not have complex multiplication.

Modular form 30899.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} + 4 q^{13} - 4 q^{14} - q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.